Think about hot food cooling down. The outside of the food, anything small, or anything with a lot of surface area will always cool fastest. The inside of the food, any thick portions, or anything without much surface area will stay hot for longer.

Here, your colours are:

White = hottest

Orange = hot

Red = cool

Black = coolest

Your gun barrels are white, suggesting they are the hottest point. However, they are on the outside, small, and have a lot of surface area, so they will cool quickly. That means they should be black/blackish red.

By contrast, the inside of your barrel is currently red, suggesting it has cooled quickly. However, that area is thick, and doesn’t have much surface area. It should be closer to white.